Stefan Kettemann

Random network models and quantum phase transitions in two dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two-dimensional Ising model is discussed. A description of renormalization group treatments is given. The classification of two-dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimensions. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.

Dimensional control of antilocalization and spin relaxation in quantum wires

The weak localization correction to the conductivity of quantum wires with linear Rashba-Dresselhaus spin-orbit coupling is derived analytically as function of wire width

Correlated persistent tunneling currents in glasses.

W

Spin-mechanical device for detection and control of spin current by nanomechanical torque

. The spin relaxation rate is found to decrease as

Localization in the quantum Hall regime

W

RKKY Interaction in Disordered Graphene

becomes smaller than the spin-precession length

Thermoelectric field effects in low-dimensional structure solar cells

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Kondo-Anderson transitions

. As a result, the sign of the conductivity correction switches to weak localization, positive magnetoconductivity for wire widths smaller than

Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants

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Nonperturbative scaling theory of free magnetic moment phases in disordered metals.

. A relaxation rate due to the cubic Dresselhaus coupling